William H. Raymond

Selective Damping in a Galerkin Method for Solving Wave Problems with Variable Grids

Abstract A dissipative Galerkin procedure is used to solve two hyperbolic problems on an irregular or variable grid. Both forced wave motions (Gaussian) and boundary induced wave propagations are considered. It is shown that results obtained by using the traditional Galerkin approximation can be improved by using the dissipative procedure. Reflections or noise produced an a grid because of mesh refinements can be substantially reduced by this technique. Comparisons are also made with the dissipative effects obtained from an added artificial viscosity term.

High-Order Low-Pass Implicit Tangent Filters for Use in Finite Area Calculations

Abstract High-order implict tangent filters are developed. The implicit tangent filters possess a highly selective amplitude response function and they can be applied relatively close to a boundary. Comparisons are made between the implict and the traditional or explict filters. Numerical simulations are performed to test the response in a limited-area model. An algorithm to maximize computing efficiency is presented. All tests indicate the desirability and utility of the implicit tangent filter.

A Review of Recursive and Implicit Filters

Abstract Low- and high-pass traditional recursive and implicit filters are reviewed. Some similarities and differences between these two forms are illustrated. The use of recursive filters in signal processing is contrasted with the needs in meteorology. The standard techniques used in building a recursive filter with specified characteristics are described. The desirability of high-order calculations is demonstrated. Some numerical results are presented to illustrate the differences in filter selectivity in the presence of topography. To make the implicit filters competitive with the traditional recursive formalism, efficient numerical matrix inversion procedures are employed in the application of both limited area and cyclic boundary conditions.

Application of Transient Turbulence Theory to Mesoscale Numerical Weather Forecasting

Abstract In this study we show that a unified turbulence parameterization, when divorced from the smoothing procedures needed for numerical stability of the host model, can be implemented in a numerical weather prediction model. Our host model is the 15-layer National Center for Atmospheric Research (NCAR)/Pennsylvania State University regional three-dimensional (3-D) primitive equation mesoscale model. The unified approach utilizes transilient turbulence theory to replace many separate empirical approximations. A sixth-order implicit tangent filter is separately applied for numerical stability of the host model. The OSCAR IV and CAPTEX datasets are used as case studies, and 72-hour forecasts are compared to control forecasts made using the original Blackadar boundary-layer version of the mesoscale model. These comparisons highlight the role of turbulence and its effect on the overall forecast. With the new turbulence parameterization we are able to produce evolving turbulent boundary layers and turbulenc...

Improved Precipitation Forecasts Using Parameterized Precipitation Drag in a Hydrostatic Forecast Model

Abstract An empirical Rayleigh drag parameterization of the nonhydrostatic mechanisms of precipitation drag and small-scale diabatically induced mixing is introduced into a hydrostatic regional forecast model to curb excessive grid-scale precipitation production. To get the needed damping, the coefficient in the Rayleigh drag is set proportional to the predicted liquid water, similar in form to the precipitation drag exhibited in nonhydrostatic calculations. The Rayleigh drag parameterization is found to be greatly superior to using the full nonhydrostatic precipitation drag term that produces a damping that is much too large in magnitude for use in a hydrostatic model. Even a rescaling of this nonhydrostatic term is found to be unsatisfactory since it lacks the sensitivity needed for hydrostatic calculations, resulting in an inability to control excessive precipitation. To incorporate nonhydrostatic vertical acceleration effects into a hydrostatic model, a modified version of the quasi-hydrostatic approx...

A Spatial Filter for Use in Finite Area Calculations

Abstract A multidimensional filter which selectively removes 2Δx and 2Δy noise is introduced. The filter is designed to be effective in finite area models with nonperiodic horizontal boundary conditions. An economical splitting technique, requiring an intermediate boundary condition, is utilized in the calculations. The filter is tested on a finite difference representation of two-dimensional linear advection and compared with the Shapiro eighth-order filter. Tests on both uniform and variable grid configurations are conducted, as well as a finite element calculation. Influence of repeated applications of the filters upon a rectangular column is analyzed and comparisons between filter factors are made. Lastly, the proposed filter is inserted into the three-dimensional Penn State-NCAR regional model to test its performance in a state-of-the-art model and to study the importance of horizontal diffusion.

Diabatic Forcing and Initialization with Assimilation of Cloud Water and Rainwater in a Forecast Model

Abstract In this study, diabatic initialization, diabatic forcing, and liquid water assimilation techniques are tested in a semi-implicit hydrostatic regional forecast model containing explicit representations of grid-scale cloud water and rainwater. Diabatic forcing, in conjunction with diabatic contributions in the initialization is found to help the forecast retain the diabatic signal found in the liquid water or heating rate data, consequently reducing the spinup time associated with grid-scale precipitation processes. Both observational Special Sensor Microwave/Imager (SSM/I) and model-generated data are used. A physical retrieval method incorporating SSM/I radiance data is utilized to estimate the 3D distribution of precipitation in storms. In the retrieval method the relationship between precipitation distributions and upwelling microwave radiances is parameterized, based upon cloud ensemble-radiative model simulations. Regression formulae relating vertically integrated liquid and ice-phase precipi...

Conservation of Moisture in a Hybrid Kuo-Type Cumulus Parameterization

Abstract The conservation of moisture requirement used in a hybrid Kuo-type cumulus parameterization scheme is generalized so that the source of moisture for the cumulus process originates from all layers below the level of condensation, including the subcloud layer(s). This conservation scheme is distinctly different than those used with the traditional Kuo-type cumulus parameterizations, which do not include convective-scale vertical transport involving the subcloud layer(s). Numerical forecasts with the modified conservation scheme are compared with those obtained using the conventional approach that extracts the moisture from the grid-scale moisture field at the level of condensation. Radiosonde observations and Geostationary Operational Environmental Satellite (GOES) observed brightness temperatures for water vapor channel 3 (6.7 μm) are used to verify the lower- and upper-tropospheric moisture fields, respectively. Forecast statistics, including precipitation as measured against rain gauge reports, ...

A Theoretical Evaluation of the Relevance of Lognormal Distributions for the Moisture Flux and Wind Components

In this study the individual components of the horizontal moist wind are derived and expressed as a function of the horizontal pressure gradients. The drag on the large-scale horizontal wind by mesoscale diabatic activity is shown to be consistent with homogeneous Lagrangian solutions that asymptotically approach a lognormal distribution. The kinematic moisture flux components are also shown to contain homogeneous solutions that behave asymptotically as a lognormal distribution. These findings are considered relevant to the large number of observed occurrences of the lognormal distribution in cloud and rainfall statistics.

Diffusion and Numerical Filters

Abstract Applications of low-pass filters or implicit diffusion are found to be extremely beneficial in a simple model problem that contains an oven-ordered advection scheme based on a symmetric stencil. In contrast, the effects are negative when either is applied to an odd-ordered approximation of advection that uses an asymmetric stencil. Also, the discriminating power of filters is shown to be helpful in identifying how small spatial-scale information influence a numerical weather prediction forecast.